Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions

Abstract

We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result.

12 pages, 10 figures

References in corpus (3)

• Worldline algorithms for Casimir configurations
• Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory
• Casimir energy in the compact QED on the lattice

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• Casimir effect in axion electrodynamics with lattice regularizations
• Dual chiral density wave induced oscillating Casimir effect
• Effective model for pure Yang-Mills theory on ${\mathbb{T}}^2\times {\mathbb{R}}^2$ with Polyakov loops
• One-quark state near a boundary of the confinement phase of QCD